Answer:
second one
Step-by-step explanation:
Answer:
Step-by-step explanation:
The first differences of the sequence are ...
- 5-2 = 3
- 10-5 = 5
- 17-10 = 7
- 26-17 = 9
- 37-26 = 11
Second differences are ...
- 5 -3 = 2
- 7 -5 = 2
- 9 -7 = 2
- 11 -9 = 2
The second differences are constant, so the sequence can be described by a second-degree polynomial.
We can write and solve three equations for the coefficients of the polynomial. Let's define the polynomial for the sequence as ...
f(n) = an^2 + bn + c
Then the first three terms of the sequence are ...
- f(1) = 2 = a·1^2 + b·1 + c
- f(2) = 5 = a·2^2 +b·2 + c
- f(3) = 10 = a·3^2 +b·3 +c
Subtracting the first equation from the other two gives ...
3a +b = 3
8a +2b = 8
Subtracting the first of these from half the second gives ...
(4a +b) -(3a +b) = (4) -(3)
a = 1 . . . . . simplify
Substituting into the first of the 2-term equations, we get ...
3·1 +b = 3
b = 0
And substituting the values for a and b into the equation for f(1), we have ...
1·1 + 0 + c = 2
c = 1
So, the formula for the sequence is ...
f(n) = n^2 + 1
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The 20th term is f(20):
f(20) = 20^2 +1 = 401
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<em>Comment on the solution</em>
It looks like this matches the solution of the "worked example" on your problem page.
Answer:
3.125
Step-by-step explanation: np
#1. 4:7 8:14 12:21
#2. 5:7 10:14 15:21
#3. 9:7 18:14 27:21
#4. 11:2 22:4 33:6
#5. 7:21 14:42 21:63
#6. 7:5 14:10 21:15
#7. Equals
#8. Equals
#9. Equals
#10 not equal
#11 not equal
# 12. Equals
#13. y=20
#14. y=14
#15. y=15
#16. y=40
#17. y=40
#18. y=36
# shared / # being shared = 5/6 Each sister gets 5/6 of a pizza.
